If HTTPS used that means that under (before) the HTTP transfer there is a secure layer (SSL or TLS). These methods are using a public/private key pair to make the encryption possible. The method ensures that no-one sitting on the lines can read the transferred data... (
HTTPS[
^]).
If you are creating a Base64 encoding of a previously encrypted data it still will be encrypted (a second time) by the secure layer included in HTTPS, however you usually do not see that encryption as it is removed by the web server (IIS) before the data sent to you. But! if you unpack and decrypt the data on the server and send back, it will be again encrypted by the HTTPS...
In the company I work for we develop a web site (some portals) that can be used with or without HTTPS - it is up to the client...however we have parts - payment related - where we force the client to use HTTPS (and from that you can understand that HTTPS can be used only for a part of your site and not for all)...
In the internet there is lot of fake and fraud, so you better not to use self signed site - that will not be accepted nicely by a majority of users, but if your customers (users) of the site are people knowing and trusting you, there is nothing wrong to sign your own site...Self-sign sites are also very good for testing and development...